OpenAI Gym: How is "experience" stored?
This is sort of a tricky question to answer, by results you could mean 2 possible things. History, which is a culmination of actions, observations and rewards. Or the value func/policy which is the thing you are trying to improve. 

With that being said, you for most instances of RL will only be dealing with the last few events in the history, or sampling uniform randomly from it according to your route of exploration. So I don't think this is what you are talking about. 

As far as storing your value func/policy OpenAI offers a way to post and to a certain extent store your result. This Readme will show you how to do so. 

Edit: OpenAI does not offer anything to store experience out of the box, as I noted in my comment you could pretty easily whip up some code that writes JSON to some file and saving that would be a store of experience. Although, it looks like you already found something that does this in tensorflow. 

OpenAI likely hasn't included it up to this point because they don't put a ton into this framework. I would encourage you check out SerpentAI on Github, as it has a lot of features missing in OpenAI.

Hope I answered your question!